Official figures show there are 64,346 households in West Sussex which qualify for a free licence.

The scheme is currently funded by the Government but the responsibility shifts to the BBC in 2020.

The broadcaster says paying for it would take a fifth of its budget and the cuts needed would ‘fundamentally change the BBC’.

A TV licence currently costs £150.50 – but is set to rise to £154.50 from April – and a review commissioned by the BBC say funding the scheme across the UK would cost £745million by 2021, rising to £1billion in a decade.

The cost of a licence for every household over 75 in West Sussex is £9.7million.

Projections from the Office for National Statistics show the growth in the aging population will mean 123,948 over-75 households in West Sussex by 2041.

The potential bill for free TV licences would be £18.7million.

Options being considered include a discount for over 75s, increasing the qualifying age to 80, or restricting free licences to the most needy.

The BBC said it wanted to hear from viewers before making a decision next summer.

Chairman David Clementi said: “We will listen to their views and balance all the options and arguments before making a decision.

“The board does not underestimate the significance of the decision, its implications for the BBC and its audiences.”

Caroline Abrahams, charity director at Age UK, said: “Despite recent progress, there are still significant numbers of older people living on very low incomes who would genuinely struggle to pay the licence fee if required to do so.

“There are two million people aged 75-plus, one-in-two of whom is disabled and one-in-four of whom view the television as their main form of companionship. For many others, including those who are chronically lonely, the TV is a precious window on the world.”

“Our initial appraisal is that any of the options set out would introduce significant practical difficulties and create unfairness for different groups of older people.”

A Department for Digital, Culture, Media and Sport spokesman said: “We know people across the country value television as a way to stay connected with the world.

“The BBC will take on responsibility for free licences for the over-75s from 2020 and it is right that they’ve confirmed no decisions will be taken until the public have been fully consulted.

“We’ve been clear that we would want and expect them to continue with this important concession. Ultimately it is the BBC’s responsibility to ensure its substantial licence fee income is used effectively to deliver fully for UK audiences.”